Evaluate the definite integral. $\int^2_{1}\left(\dfrac{12}{x^2}-1\right)\,dx = $
Solution: First, use the power rule: $\begin{aligned}\int^2_{1}\left(\dfrac{12}{x^2}-1\right)\,dx~&=\int^2_{1}\left(12x^{-2}-1\right)\,dx \\&=~(-12x^{-1}-x)\Bigg|^2_{1}\end{aligned}$ Second, plug in the limits of integration: $[-12\cdot2^{-1}-2]-[-12\cdot1^{-1}-1] = -8+13 = 5$. The answer: $\int^2_{1}\left(\dfrac{12}{x^2}-1\right)\,dx = 5$